We present a novel computational formulation of speaker authority in discourse. This notion, which focuses on how speakers position themselves relative to each other in discourse, is ﬁrst developed into a reliable coding scheme (0.71 agreement between human annotators). We also provide a computational model for automatically annotating text using this coding scheme, using supervised learning enhanced by constraints implemented with Integer Linear Programming.

The ability to compress sentences while preserving their grammaticality and most of their meaning has recently received much attention. Our work views sentence compression as an optimisation problem. We develop an integer programming formulation and infer globally optimal compressions in the face of linguistically motivated constraints. We show that such a formulation allows for relatively simple and knowledge-lean compression models that do not require parallel corpora or largescale resources. The proposed approach yields results comparable and in some cases superior to state-of-the-art.

In this paper, we present a formalization of grammatical role labeling within the framework of Integer Linear Programming (ILP). We focus on the integration of subcategorization information into the decision making process. We present a ﬁrst empirical evaluation that achieves competitive precision and recall rates.

This paper pro -poses two ideas for adapting standard kinematic techniques to situations that do not naturally allow for the constraint of a fixed baseline. The first calls for extracting the information needed to resolve the integer ambiguity from the very data collected while the kinematic survey is in progress. The second idea addresses the use of the antenna exchange technique for mobile platforms where the original locations of
the antennas are not likely to remain stationary during the physical exchange.

Let b ≥ 2 be an integer. We prove that the b-ary expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic numbers are transcendental, for a wide class of morphisms. In particular, irrational automatic numbers are transcendental. Our main tool is a new, combinatorial transcendence criterion. 1. Introduction Let b ≥ 2 be an integer. The b-ary expansion of every rational number is eventually periodic, but what can be said about the b-ary expansion of an irrational algebraic number? ...

We determine the order of magnitude of H(x, y, z), the number of integers n ≤ x having a divisor in (y, z], for all x, y and z. We also study Hr (x, y, z), the number of integers n ≤ x having exactly r divisors in (y, z]. When r = 1 we establish the order of magnitude of H1 (x, y, z) for all x, y, z satisfying z ≤ x1/2−ε . For every r ≥ 2, C 1 and ε 0, we determine the order of magnitude of Hr (x, y, z) uniformly...

In 1991, David Gale and Raphael Robinson, building on explorations carried out by Michael Somos in the 1980s, introduced a three-parameter family of rational recurrence relations, each of which (with suitable initial conditions) appeared to give rise to a sequence of integers, even though a priori the recurrence might produce non-integral rational numbers. Throughout the '90s, proofs of integrality were known only for individual special cases. In the early '00s, Sergey Fomin and Andrei Zelevinsky proved Gale and Robinson's integrality conjecture.